Yaolin Yu | Searcharxiv

arXiv2026

Continuous stochastic flows driven by white noise and their duals

We study a class of continuous stochastic flows driven by a space-time white noise and characterize their dual flows by explicit stochastic differential equations. A key ingredient of the proof is the convergence of solutions under coefficient approximations. As an application, we derive the dual flows in two illustrative examples, the squared Bessel flow and the Jacobi flow. We also introduce a new model of polynomially self-repelling (PSR) flow and show that it enjoys a self-duality property.

math.PR↗

arXiv2024

Meeting of squared Bessel flow lines and application to the skew Brownian motion

We study the meeting level between squared Bessel (BESQ) flow lines of different dimensions, and show that it gives rise to a jump Markov process. We apply these results to the skew Brownian flow introduced by Burdzy and Chen \cite{burdzy2001local} and Burdzy and Kaspi \cite{burdzy2004lenses}. It allows us to extend the results of \cite{burdzy2001local} and of Gloter and Martinez \cite{gloter2013distance} describing the local time flow of skew Brownian motions. Finally, we compute the Hausdorff dimension of exceptional times revealed by Burdzy and Kaspi \cite{burdzy2004lenses} when skew Brownian flow lines bifurcate.

math.PR↗